Eur. Phys. J. Plus (2016) 131: 437
https://doi.org/10.1140/epjp/i2016-16437-3

Regular Article

Influence of the combined effect of magnetic field and rotation on the onset of a non-Newtonian viscoelastic nanofluid layer: Linear and nonlinear analyses

¹ Department of Mathematics, North Cap University, Gurgaon, India
² Department of Mathematics, Jaypee Institute of Information Technology, Noida, India

^* e-mail: puneetranaiitr@gmail.com

Received: 27 August 2016
Accepted: 13 November 2016
Published online: 22 December 2016

Abstract

In the present paper, we present both linear and nonlinear analyses to investigate thermal instability on a rotating non-Newtonian viscoelastic nanofluid layer under the influence of a magnetic field. In the linear stability analysis, the stationary and oscillatory modes of convection are obtained for various controlling parameters using the normal mode technique. Both Nusselt and Sherwood numbers are calculated after employing the minimal truncated Fourier series to steady and unsteady state. The main findings conclude that rotation and strain retardation parameter increase the value of the critical Rayleigh number in the neutral stability curve which delays the onset of convection in the nanofluid layer while the stress relaxation parameter enhances the convection. The magnetic field stabilizes the system for low values of the Taylor number (rotation) but an inverse trend is observed for high Taylor number. Both Nusselt and Sherwood numbers initially oscillate with time until the steady state prevails and they decrease with both Chandrasekhar and Taylor numbers. The magnitude of the streamlines and the contours of both isotherms and iso-nanohalines concentrate near the boundaries for large values of Ra, indicating an increase in convection.